The Galileon as a Local Modification of Gravity The Galileon model is a local modification of gravity that introduces a relativistic scalar field, π, universally coupled to matter and with specific derivative self-interactions. This model is studied to understand the connection between self-acceleration and the presence of ghosts in theories modifying gravity in the infrared. The Galileon model is defined as those that reduce to a generalization of the DGP 4D effective theory at distances shorter than cosmological. The model is argued to be the only one that allows for a robust implementation of the Vainshtein effect, which decouples the scalar from matter in gravitationally bound systems. The model involves an internal Galilean invariance, under which π's gradient shifts by a constant. This symmetry constrains the structure of the π Lagrangian so that in 4D, only five terms can yield sizable non-linearities without introducing ghosts. The model shows that for such theories, there are self-accelerating deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are stable against small fluctuations. The model is investigated for possible infrared completions at scales of order the Hubble horizon. However, the model has some features that may be problematic at the theoretical or phenomenological level: the presence of superluminal excitations; the extreme sub-luminality of other excitations, which makes the quasi-static approximation for certain solar-system observables unreliable due to Cherenkov emission; and the very low strong-interaction scale for ππ scatterings. The model is shown to have a robust implementation of the Vainshtein effect, and the existence of self-accelerating solutions with no ghost-like instabilities. The model is also shown to have spherically symmetric solutions that describe the π field generated by compact sources, which are ghost-free. The model is found to have a radial solution for all r's, which constrains the coefficients to some extent. The model is also found to have a stable solution against small perturbations, with all the K_i's positive. The model is found to have subluminal propagation speeds for angular excitations, but superluminal propagation speeds for radial excitations at large distances from the source. The model is found to have constraints on the coefficients to ensure stability and subluminal propagation speeds. The model is found to have a robust implementation of the Vainshtein effect, and the existence of self-accelerating solutions with no ghost-like instabilities. The model is found to have spherically symmetric solutions that describe the π field generated by compact sources, which are ghost-free. The model is found to have a radial solution for all r's, which constrains the coefficients to some extent. The model is found to haveThe Galileon as a Local Modification of Gravity The Galileon model is a local modification of gravity that introduces a relativistic scalar field, π, universally coupled to matter and with specific derivative self-interactions. This model is studied to understand the connection between self-acceleration and the presence of ghosts in theories modifying gravity in the infrared. The Galileon model is defined as those that reduce to a generalization of the DGP 4D effective theory at distances shorter than cosmological. The model is argued to be the only one that allows for a robust implementation of the Vainshtein effect, which decouples the scalar from matter in gravitationally bound systems. The model involves an internal Galilean invariance, under which π's gradient shifts by a constant. This symmetry constrains the structure of the π Lagrangian so that in 4D, only five terms can yield sizable non-linearities without introducing ghosts. The model shows that for such theories, there are self-accelerating deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are stable against small fluctuations. The model is investigated for possible infrared completions at scales of order the Hubble horizon. However, the model has some features that may be problematic at the theoretical or phenomenological level: the presence of superluminal excitations; the extreme sub-luminality of other excitations, which makes the quasi-static approximation for certain solar-system observables unreliable due to Cherenkov emission; and the very low strong-interaction scale for ππ scatterings. The model is shown to have a robust implementation of the Vainshtein effect, and the existence of self-accelerating solutions with no ghost-like instabilities. The model is also shown to have spherically symmetric solutions that describe the π field generated by compact sources, which are ghost-free. The model is found to have a radial solution for all r's, which constrains the coefficients to some extent. The model is also found to have a stable solution against small perturbations, with all the K_i's positive. The model is found to have subluminal propagation speeds for angular excitations, but superluminal propagation speeds for radial excitations at large distances from the source. The model is found to have constraints on the coefficients to ensure stability and subluminal propagation speeds. The model is found to have a robust implementation of the Vainshtein effect, and the existence of self-accelerating solutions with no ghost-like instabilities. The model is found to have spherically symmetric solutions that describe the π field generated by compact sources, which are ghost-free. The model is found to have a radial solution for all r's, which constrains the coefficients to some extent. The model is found to have